MoeaBench v0.8.0 Technical Calibration Report

Scientific Performance Audit and Convergence Metrics

1. Methodology & Experimental Context

This report serves as the official scientific audit for MoeaBench v0.8.0. The objective is to validate and calibrate the numerical integrity and topological fidelity of the framework's core algorithms against established mathematical benchmarks (Ground Truth).

Experimental Setup

2. Metric Glossary & Interpretation

Scientific Note: The Discretization Effect & Negative H_diff
In cases of near-perfect convergence, you may observe an H_rel exceeding 100%.

DTLZ1 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.3076 (Eff: 22.02x)3.1689e-01 ± 1.4e+001.6218e-02 ± 9.9e-030.0585 (Eff: 6.50x)1.31850.990699.09%117.98Gen 500
NSGA20.0493 (Eff: 3.53x)2.4803e-01 ± 1.5e+004.3729e-02 ± 2.3e-010.0547 (Eff: 6.08x)1.33101.0000100.02%87.18Gen 300
NSGA30.0298 (Eff: 2.13x)1.4113e-02 ± 2.0e-032.7772e-03 ± 9.2e-030.0543 (Eff: 6.03x)1.26420.949899.73%13.09Gen 200

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DTLZ2 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.0394 (Eff: 1.04x)1.8089e-02 ± 8.2e-048.2981e-03 ± 8.8e-030.0991 (Eff: 5.24x)0.77390.581597.11%118.74Gen 100
NSGA20.0312 (Eff: 0.82x)1.8039e-02 ± 8.3e-041.6873e-02 ± 9.1e-030.0828 (Eff: 4.38x)0.83110.624497.46%80.07Gen 100
NSGA30.0398 (Eff: 1.05x)1.6911e-02 ± 1.4e-047.1919e-03 ± 8.7e-030.0991 (Eff: 5.23x)0.76630.575796.90%13.27Gen 100

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DTLZ3 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.5402 (Eff: 14.20x)1.6522e+00 ± 1.1e+002.1422e-01 ± 2.8e-020.3004 (Eff: 15.49x)1.28290.963996.56%112.82Gen 1000
NSGA20.5989 (Eff: 15.75x)2.3090e+00 ± 1.4e+011.5829e-01 ± 8.7e-010.0976 (Eff: 5.03x)1.33101.0000100.00%84.55Gen 400
NSGA30.4198 (Eff: 11.04x)5.4060e-01 ± 1.7e+001.6181e-01 ± 5.1e-010.1087 (Eff: 5.61x)1.33090.999999.99%12.43Gen 600

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DTLZ4 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.0349 (Eff: 0.92x)1.8882e-02 ± 1.3e-031.3461e-02 ± 7.7e-030.2163 (Eff: 10.22x)0.77050.578997.98%112.80Gen 100
NSGA20.0326 (Eff: 0.86x)1.7482e-02 ± 6.3e-041.8044e-02 ± 8.7e-030.1038 (Eff: 4.91x)0.83140.624797.26%77.83Gen 100
NSGA30.0398 (Eff: 1.05x)1.6920e-02 ± 4.3e-047.2102e-03 ± 8.7e-030.1085 (Eff: 5.13x)0.77180.579997.06%12.55Gen 100

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DTLZ5 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.0068 (Eff: 2.11x)6.5874e-04 ± 3.8e-045.2277e-03 ± 8.3e-030.2260 (Eff: 18.29x)0.42060.316098.91%111.16Gen 100
NSGA20.0019 (Eff: 0.59x)7.9038e-04 ± 1.9e-041.7806e-03 ± 1.3e-030.0271 (Eff: 2.19x)0.26910.202299.65%82.41Gen 300
NSGA30.0038 (Eff: 1.19x)4.9039e-04 ± 3.3e-052.6192e-03 ± 2.2e-030.0951 (Eff: 7.69x)0.26920.202399.16%11.83Gen 100

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DTLZ6 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.0560 (Eff: 17.41x)8.9077e-02 ± 2.6e-021.5905e-02 ± 1.2e-020.2369 (Eff: 17.85x)0.62510.469693.81%112.39Gen 200
NSGA20.1586 (Eff: 49.34x)2.0389e-01 ± 5.9e-011.0132e-02 ± 1.7e-020.0569 (Eff: 4.29x)1.26650.951699.07%76.78Gen 400
NSGA30.1930 (Eff: 60.05x)2.4915e-01 ± 6.0e-011.6877e-02 ± 1.8e-020.1609 (Eff: 12.12x)1.24590.936098.39%14.64Gen 600

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DTLZ7 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.0928 (Eff: 2.99x)2.2038e-02 ± 1.7e-030.0000e+00 ± 0.0e+000.5379 (Eff: 21.65x)0.00000.00000.00%10.00Gen 200
NSGA20.0340 (Eff: 1.09x)2.0875e-02 ± 3.9e-033.4321e-02 ± 4.3e-030.0769 (Eff: 3.10x)0.68850.517396.53%76.05Gen 200
NSGA30.1128 (Eff: 3.63x)2.2767e-02 ± 6.6e-030.0000e+00 ± 0.0e+000.0743 (Eff: 2.99x)0.00000.00000.00%10.00Gen 300

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DTLZ8 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
NSGA2840.6049 (Eff: 30620.57x)8.4035e+02 ± 1.0e+031.1544e-03 ± 2.2e-030.2982 (Eff: 20.23x)0.79900.600360.03%30.89Gen 500
NSGA30.0490 (Eff: 1.79x)1.6853e-02 ± 9.9e-041.7490e-02 ± 1.7e-030.0187 (Eff: 1.27x)0.97240.730694.99%15.26Gen 500

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DTLZ9 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
NSGA21730.8555 (Eff: 439604.50x)1.7308e+03 ± 0.0e+000.0000e+00 ± 0.0e+00999.3098 (Eff: 67111.57x)0.00100.00080.08%12.75Gen 100
NSGA30.2067 (Eff: 52.50x)6.6958e-02 ± 6.7e-038.3061e-03 ± 1.0e-030.2184 (Eff: 14.67x)0.14610.109854.21%15.08Gen 500

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DPF1 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.3479 (Eff: 204.64x)3.1650e-01 ± 9.8e-015.1073e-03 ± 2.4e-030.0606 (Eff: 9.58x)1.21750.914794.40%117.58Gen 500
NSGA20.0051 (Eff: 2.99x)2.3259e-02 ± 1.4e-011.3109e-03 ± 3.0e-030.0043 (Eff: 0.67x)1.17200.880599.83%82.37Gen 400
NSGA30.0937 (Eff: 55.14x)9.7682e-02 ± 4.5e-011.6700e-03 ± 1.3e-030.0421 (Eff: 6.66x)1.20420.904897.41%12.23Gen 400

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DPF2 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.9019 (Eff: 55.00x)4.0960e-05 ± 4.5e-073.5453e-03 ± 8.4e-061.7520 (Eff: 35.05x)0.19210.144349.90%115.59Gen 100
NSGA20.0017 (Eff: 0.11x)1.2828e-04 ± 2.0e-051.0080e-02 ± 8.1e-030.2300 (Eff: 4.60x)0.38410.288699.72%72.52Gen 100
NSGA30.0031 (Eff: 0.19x)1.2220e-04 ± 1.5e-051.4596e-02 ± 1.2e-020.5447 (Eff: 10.90x)0.38440.288899.54%13.38Gen 200

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DPF3 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
NSGA20.0016 (Eff: 0.58x)3.0564e-03 ± 1.2e-042.0067e-03 ± 1.4e-030.2914 (Eff: 55.12x)0.79450.5969100.22%75.93Gen 800
NSGA30.0042 (Eff: 1.54x)3.1938e-03 ± 1.6e-043.0014e-03 ± 2.3e-030.3242 (Eff: 61.32x)0.79820.599799.99%12.23Gen 100

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DPF4 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.5025 (Eff: 120.58x)1.4101e-01 ± 7.8e-018.9064e-04 ± 1.6e-030.1243 (Eff: 11.41x)0.69490.522153.27%121.37Gen 300
NSGA20.0044 (Eff: 1.05x)2.4544e-02 ± 1.5e-013.3861e-03 ± 3.4e-030.0142 (Eff: 1.31x)1.16320.873999.64%82.92Gen 200
NSGA30.0233 (Eff: 5.59x)1.8991e-02 ± 1.2e-011.3051e-02 ± 4.9e-020.0426 (Eff: 3.91x)1.30610.981399.68%12.23Gen 200

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x

DPF5 Benchmark Analysis

AlgorithmIGD (Mean ± Std)GD (Mean ± Std)SP (Mean ± Std)EMD (Wasserstein)H_rawH_ratioH_relTime(s)Stabil.
MOEAD0.0304 (Eff: 1.60x)6.7792e-03 ± 1.4e-041.6212e-02 ± 2.0e-020.1130 (Eff: 5.93x)0.70660.530996.80%113.39Gen 100
NSGA20.0142 (Eff: 0.75x)9.1868e-03 ± 4.9e-032.0535e-02 ± 8.9e-030.1023 (Eff: 5.38x)1.10820.832699.13%81.79Gen 100
NSGA30.0239 (Eff: 1.26x)6.2888e-03 ± 1.8e-041.8744e-02 ± 1.0e-020.2093 (Eff: 11.00x)0.78850.592497.87%12.51Gen 200

Certification & Pathology Matrix

AlgorithmGeometry StatusEXPLORATORY INDUSTRY STANDARD RESEARCH
MOEADIDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA2IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
NSGA3IDEAL_FRONT
Ideal Front. Excellent convergence, purity, and topology.
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x
PASS
IGD_eff=1.00x, EMD_eff=0.00x